Question

Vector h points true north and has a magnitude of 3 units. Vector k points 45° east of true north. Write k-h in magnitude and direction form if k-h points directly east.

Answer 1

Therefore, the vector k-h cannot be written in magnitude and direction form if k-h points directly east.

Explanation:

To write the vector k-h in magnitude and direction form, we first need to find the magnitude and direction of the vector k-h.

Magnitude:

The magnitude of a vector is the length or size of the vector. To find the magnitude of k-h, we subtract the magnitude of h from the magnitude of k.

Given that the magnitude of h is 3 units, we need to find the magnitude of k.

Since k points 45° east of true north and k-h points directly east, we can visualize a right triangle with the vectors k, h, and k-h. The angle between k and k-h is 90°, and the angle between h and k-h is 45°.

To find the magnitude of k, we can use the Pythagorean theorem:

k^2 = h^2 + (k-h)^2

Substituting the given values:

k^2 = 3^2 + (k-h)^2

Simplifying the equation:

k^2 = 9 + (k-h)^2

Since k-h points directly east, the horizontal component of k-h is equal to the magnitude of k.

k^2 = 9 + k^2

Simplifying further:

0 = 9

This equation is not possible, which means there is no magnitude for the vector k-h that satisfies the condition of k-h pointing directly east.